Chapter 2 Honors Physics Max Llewellyn

Constant Speed

Basic Terms

Week 1 - 9/5 to 9/9

9/7/2011 Homework 1D Kinematics

1. What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
   1. The difference between speed and velocity, that speed is a rate of motion in any number of unspecified direction(s) but velocity is rate of motion in a specific direction.
   2. The difference between distance and displacement, that distance is total length traveled and displacement is amount of length relative to a position.
2. What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding.
   1. There wasn't much covered in class and I understood all of it at the end of class.
3. What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
   1. There wasn't anything in the reading that we didn't cover in class, see above.
4. What (specifically) did you read that was not gone over during class today?
   1. Vectors and scallers could refer to more then objects and motion eg: bytes, calories, temperature.

9/8/2011 Classnotes Types of Motion

1. Types of motion
   1. at rest - no acceleration
      1. v = 0, a = 0
   2. constant speed - no acceleration
      1. show with Vs above arrows -v-> -v-> -v-> that are all the same size, a = 0
   3. increasing speed - yes acceleration
      1. shown with Vs above arrows that get bigger -v-> -V->
      2. Arrow above an a pointing forward -a->
   4. decreasing speed - yes -acceleration
      1. shown with Vs above arrows that get smaller -V-> -v->
      2. Arrow above an a pointing backward <-a-
2. Acceleration is a change in velocity, speeding up OR slowing down

9/8/2011 Homework Describing motion with Diagrams

1. What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
   1. How a ticker tape diagram works, by placing a mark on a tape fastened to an object at a constant time interval.
   2. How to read a ticker tape diagram by measuring the difference between the marks on the tape.
2. What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding.
   1. That in a vector diagram the arrow gets large to indicate acceleration, I previously thought the V got larger.
3. What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
   1. There was nothing I read that I didn't understand.
4. What (specifically) did you read that was not gone over during class today?
   1. That a ticker tape diagram could also be referred to as an oil drop diagram.

9/9/2011 Lab The Speed of a CMV (Constant Motion Vehicle)

Objectives; be able to answer these questions

1. How precisely can you measure distances with a meter stick?
2. how fast does your CMV move?
3. What information can you get from a position-time graph?

Materials: spark timer, spark tape, meter stick, masking tape, CMV

Hypotheses

1. I can measure distance with a meter stick down to units of .5 cm with a +-.2 cm margin of error, down to units of .1mm if there are mm marks with +-.3.4 mm margin of error
2. The CMV moves approximately 13.75 cm / 1 s
3. I can get average and instantaneous speed, position at a given time from a position-time graph

Work

1. Length of laptop 32.80 cm
2. 
3. CMV Lab Excel sheet
   

   CMV lab.xlsx
   

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4. 

Discussion Questions

1. Why is the slope of the position-time graph equivalent to average velocity?
   1. Velocity is the rate of change in position over change in time, slope is ∆Y/∆X. Because the Y value on a position-time graph is position and X is time, ∆Y/∆X is the same as change in position over change in time is the same as velocity.
2. Why is it average velocity and not instantaneous velocity? What assumptions are we making?
   1. We are assuming that the CMV was at a constant velocity that never changed. Therefor instantaneous velocity at any given point would be the same as average velocity.
3. Why was it okay to set the y-intercept equal to zero?
   1. Since the CMV moved at a constant rate and there was no acceleration the difference between any two dots on the spark tape should be the same so anyone can function as an effective 0.
4. What is the meaning of the R2 value?
   1. The R^2 value represents how close a data plotted resembles a line plotted with only the equation given.
5. If you were to add the graph of another CMV that moved more slowly on the same axes as your current graph, how would you expect it to lie relative to yours?
   1. I would expect it to also be a straight line with a slope less then my line.

Conclusion

We found that our CMV went 31.875 mm/s based on plots pointed and a graph and a slope calculated by a trend line by Microsoft Excel.

There are several sources of error that could have contributed to our .99998 R^2 value, while we did start the cart before starting the timer we did not ignore any of the dots on the spark tape past the first one because we assumed the car was already at speed, which it might not have been. While we did only measure the difference between the dots and calculate the sum we did use a hard ruler while a soft ruler on the warped floor could have been more accurate. Also, while the CMV could have been at a constant speed a warped floor would have decreased it's speed relative to a straight axis, what the spark tape was measuring.

Accelerated Motion

Week 2 - 9/12 to 9/16

9/12/2011 Activity Graphical Representations of Equilibrium

Objectives

• What is the difference between static and dynamic equilibrium?
• How is “at rest” represented on a position vs. time graph? On a velocity vs. time graph? On an acceleration vs. time graph?
• How is constant speed represented on a position vs. time graph? On a velocity vs. time graph? On an acceleration vs. time graph?
• How are changes in direction represented on a position vs. time graph? On a velocity vs. time graph? On an acceleration vs. time graph?

Our graphs
At rest


Constant motion away


Constant motion closer


Discussion Questions

1. How can you tell that there is no motion on a…
   1. position vs. time graph
      1. the Y value is 0
   2. velocity vs. time graph
      1. the Y value is 0
   3. acceleration vs. time graph
      1. you can't
2. How can you tell that your motion is steady on a…
   1. position vs. time graph
      1. the line has a constant slope
   2. velocity vs. time graph
      1. the Y axis is static
   3. acceleration vs. time graph
      1. the Y value is 0
3. How can you tell that your motion is fast vs. slow on a…
   1. position vs. time graph
      1. the slope of the line is large
   2. velocity vs. time graph
      1. the Y value is high
   3. acceleration vs. time graph
      1. you can't

1. How can you tell that you changed direction on a…
   1. position vs. time graph
      1. the slope of the line passed 0 (up or down)
   2. velocity vs. time graph
      1. the Y value passed the X axis
   3. acceleration vs. time graph
      1. the Y value passed the X axis

1. What are the advantages of representing motion using a…
   1. position vs. time graph
      1. you have the most information of all of the graphs, you can calculate velocity and acceleration and know position
   2. velocity vs. time graph
      1. it is very easy to determine the speed and direction of the object being graphed, acceleration can be calculated
   3. acceleration vs. time graph
      1. it is very easy to see the change in velocity

1. What are the disadvantages of representing motion using a…
   1. position vs. time graph
      1. velocity and acceleration must be calculated
   2. velocity vs. time graph
      1. position can not be determined, acceleration must be calculated
   3. acceleration vs. time graph
      1. neither position or velocity can be calculated

1. Define the following:
   1. No motion
      1. Velocity is 0, position is constant, acceleration is 0
   2. Constant speed
      1. acceleration is 0, position changed at a constant rate, velocity is static

The Big 5

9/13/2011 In Class Notes 5 big equations

V = ∆d/∆t ONLY works when speed is constant or you're looking for an average
you can also just take an average, V = (V1 + V2) / 2
play with the equations and you get ∆d = .5(V1 + V2)∆t

acceleration is rate of change in speed
a = (Vf - Vi) / ∆t; Vf = velocity final; Vi = velocity initial
Vf = Vi +a∆t
∆d = .5(Vi+Vf)∆t
∆d = Vi∆t + .5a∆t^2
Vf^2 = Fi^2 + 2ad

9/13/2011 Homework Acceleration

1. What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
   1. Negative acceleration, or acceleration in the opposite direction of movement, is the same as slowing down
   2. Average acceleration is equal to ∆velocity (of Vfinal - Vinitial) over ∆time
2. What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding.
   1. I didn't have any conceptions about acceleration that differed from what I read.
3. What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
   1. I understood everything covered in the section.
4. What (specifically) did you read that was not gone over during class today?
   1. There was nothing mentioned that wasn't gone over in class.

9/14/2011 Homework 1D Kinematics lessons 3 & 4

1. What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
   1. The slope of a line is nearly the same of the velocity of the object being graphed.
   2. A increasing velocity rightward looks like a curve with the 'bump' on the bottom right, visa versa for a increasing velocity leftward.
2. What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding.
   1. Due to the amazing quality of which the lesson was taught there was nothing I read that I didn't already understand.
3. What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
   1. I understood everything covered in the reading. (what animal is the yellow character suppose to be and what is it's facial expression?)
4. What (specifically) did you read that was not gone over during class today?
   1. The only thing not covered in class was the basic algebra required to calculate slope.

1. What (specifically) did you read that you already understood well from our class discussion? Describe at least 2 items fully.
   1. That an increasing slope on a v-t graph shows acceleration, and a constant slope shows constant speed, a - slope shows -acceleration.
   2. Once the line on a v-t graph passed the X axis the direction of motion changes, at 0 is at rest.
2. What (specifically) did you read that you were a little confused/unclear/shaky about from class, but the reading helped to clarify? Describe the misconception you were having as well as your new understanding.
   1. I didn't think of using area to calculate position at any given time on a v-t graph.
3. What (specifically) did you read that you still don’t understand? Please word these in the form of a question.
   1. I usenderstood everything covered in the reading.
4. What (specifically) did you read that was not gone over during class today?
   1. The area under a v-t graph (integral) is equal to position, and the basic algebra area formulas.

Graphing

9/15/2011 Classwork XXX


A. The graph below shows the motion of a car.

1. Describe the motion of the car (qualitatively) during each segment.
   1. At rest
   2. Constant speed back to origin
   3. At rest
   4. Fast constant speed away from origin
   5. At rest
   6. Constant to origin
   7. Increases speed away from origin
2. Describe the change in position of the car during each segment.
   1. 0m
   2. -10m
   3. 0m
   4. -16m
   5. 0m
   6. 16m
   7. 14m
3. Calculate the velocity of the car during each segment.
   1. 0
   2. -5 m/s
   3. 0
   4. -32 m/s
   5. 0
   6. 16 m/s
   7. 12 m/s
4. What is its average speed for the entire 12-s?
   1. total distance / total time
   2. 0+10+0+16+0+16+14 / 11
   3. 56 / 11
   4. 5.09
5. What is its average velocity for the entire 12-s?
   1. 14-10 / 11
   2. 4 / 11
   3. 0.36
6. What is the acceleration of the car during each segment?
   1. 0 (aside form the little pockets of impossible instantaneous acceleration)
7. Sketch a v-t graph that corresponds to this p-t graph.
   1. 
      

B. The graph below shows the motion of a helicopter. (Label each endpoint with a letter, beginning with A at 0 s, B at 1 s, C at 2 s, D at 4 s, E at 5 s, F at 7 s, G at 8 s, H at 10 s.)

1. Describe the motion of the car (qualitatively) during each segment.
2. Describe the in position of the car during each segment.
3. Calculate the velocity of the car during each segment.
4. What is its average speed for the entire 10-s?
5. What is its average velocity for the entire 10-s?
6. What is the acceleration of the car during each segment?
7. Sketch a v-t graph that corresponds to this x-t graph.

C. The graph below shows the motion of an airplane. (Label each endpoint with a letter, beginning with A at (0,0) and ending with E at (100,0).)

1. Describe the motion of the car (qualitatively) during each segment.
2. Describe the change in position of the car during each segment.
3. Calculate the velocity of the car during each segment.
4. What is its average speed for the entire 100-s?
5. What is its average velocity for the entire 100-s?
6. What is the acceleration of the car during each segment?
7. Sketch a v-t graph of the motion shown in the x-t graph.

D. The graph below shows an x-t graph.

1. Describe the motion of the object (qualitatively).
   1. accelerating
2. Calculate the instantaneous velocity of the car at 0.2 seconds.
   1. 170 cm/s
3. Calculate the instantaneous velocity of the car at 0.4 seconds.
   1. 380 cm/s
4. What is its average speed for the entire 0.5-s?
   1. 240 cm/s
5. Sketch a v-t graph of the motion shown in the x-t graph.

E. The graph below shows an x-t graph.

1. Describe the motion of the object (qualitatively).
   1. going fast and slowing down away until the object begins to go backwards and accelerate toward the origin.
2. Calculate the instantaneous velocity of the car at 1 seconds.
   1. 32.5 cm/s
3. Calculate the instantaneous velocity of the car at 2.5 seconds.
   1. 0
4. Calculate the instantaneous velocity of the car at 5 seconds.
   1. 53 cm/s
5. What is its average velocity for the entire 0.5-s?
   1. 0 cm/s
6. Sketch a v-t graph of the motion shown in the x-t graph.

F. The graph below represents a boy riding his bicycle with his friends around town after school. Express all answers in km/hr.

1. How fast is the boy moving during Segment AB?
2. How fast is the boy moving during Segment BC?
3. How fast is the boy moving during Segment CD?
4. What is the boy's average speed for the entire trip? His average velocity?
5. If the boy spent the last 15 minutes (not shown on the graph) pedaling all the way back home, what is his average velocity for the entire hour?
6. Sketch a v-t graph that corresponds to this x-t graph.

G. The graph below represents a boy riding his bicycle with his friends around town after school. Express all answers in m/s.

1. How fast is the boy moving during the time interval from 0-10 seconds?
2. How fast is the boy moving during the time interval from 10-15 seconds?
3. How fast is the boy moving during the time interval from 15-40 seconds?
4. How fast is the boy moving during the time interval from 40-60 seconds?
5. What is the boy's average speed for the time interval from 0-40 seconds?
6. What is his average speed for the entire hour?
7. What is his average velocity for the entire hour?
8. Sketch a v-t graph that corresponds to this x-t graph.

9/16/2011 Lab Acceleration Graphs

-With the young and beautiful Ryan Luo

• Objective(s) and Hypotheses
  • What does a position-time graph for increasing speeds look like?
    • Similar to the right portion of a graph of the line X^2
  • What information can be found from the graph?
    • Position, velocity and acceleration can be gathered from the graph
• Procedure and Materials
  • Spark tape, spark timer, , dynamics cart,
• Data and Graph(s)
  • Graphs
    • 
  • Data (note: some of the data is scrap work done with excel equations)
    • 
  • More data
    

    Acceleration graphs.xlsx
    

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• Analysis:
  • a) Interpret the equation of the line (slope, y-intercept) and the R2 value.
    • The R^2 value for the linear trend lines (.9228, .87654) was extremely low compared to the polynomial trend line R^2 values (.99959, .99778), also we knew that acceleration wasn't linear so we used a polynomial trend line instead of a linear one.
  • b) Find the instantaneous speed at halfway point and at the end. (You may find this easier to do on a printed copy of the graph. Just remember to take a snapshot of it and upload to wiki when you are done.)
    • Used tangent line in excel
    • Halfway - 36.039 cm/s
    • End - 69.787 cm/s
  • c) Find the average speed for the entire trip.
    • 75.85cm / 2s = 37.925 cm/s
• Discussion Questions:
  • 1. What would your graph look like if the incline had been steeper?
    • the A value would have been higher ie:50x^2 instead of 17x^2
  • 2. What would your graph look like if the cart had been decreasing up the incline?
    • It would look similar to the left half of the line -(x^2) although MUCH shallower
  • 3. Compare the instantaneous speed at the halfway point with the average speed of the entire trip.
    • They are nearly the same, I think they would be exactly the same if my math was better
  • 5. Draw a v-t graph of the motion of the cart. Be as quantitative as possible.
    • It would be a straight line with a constant slope. This data was calculated with a modified excel equation for a line tangent to a point on the line of the positive acceleration graph.
    • 
• Conclusion
  • We found that our hypotheses were accurate. The graph was a polynomial and looked like we thought it would and we were able to gather or calculate all the data and information we thought we could. There were many sources of error but I believe the largest was that the first mark on the spark tape was not necessarily in sync with when the vehicle started moving. We could minimize this error by having a computer controlled spark timer and release system for the vehicle.

Week 3 - 9/19 to 9/23

9/21/2011 Class Notes Catching up problems

1. A car is behind a truck going 30 m/s on the highway. The car’s driver looks for an opportunity to pass, guessing that his car can accelerate at 2 m/s2. He gauges that he has to cover the 15-m length of the truck, plus 10 m clear room at the rear of the truck and 10-m more at the front of it. In the oncoming lane, he sees a car approaching, probably traveling at 20 m/s. He estimates that the car is about 450-m away. Should he attempt the pass? (requires a minimum of 330.9 m, so yes)
   1. yes, can pass
2. A car is behind another car going 30 m/s on the highway. The car’s driver looks for an opportunity to pass, guessing that his car can accelerate at 2 m/s2. He gauges that he has to cover the 10-m length of the car, plus 8 m clear room at the rear of the car and 8-m more at the front of it. In the oncoming lane, he sees a car approaching, probably traveling at 25 m/s. He estimates that the car is about 350-m away. Should he attempt the pass? (requires a minimum of 306.5 m, so yes)
   1. yes, can pass
3. A runner hopes to complete a 5-km run in less than 16.0 minutes. After exactly 13.0 min, there are still 500 m to go. The runner must then accelerate at 0.25 m/s2 for how many seconds in order to achieve the desired time? (372 s, not possible!)

9/23/2011 Lab A Crash Course in Velocity (Part II)

Staring Max Llewellyn and the beautiful and talented Ryan Luo. Guest starring the gorgeous and adept XXX

CMVs; our group 31.875 cm/s , other group 58.021 cm/s

1. Find the position where both CMV’s will meet if they start at least600 cm apart, move towards each other, and start simultaneously.
   1. Equation:
      1. Vcmv1*T + Vcmv2*T = Distance-apart
      2. T*(Vcmv1 + Vcmv2) = Distance-apart
      3. Distance-apart / (Vcmv1 + Vcmv2) = T
      4. (equation #3 with numbers plugged in) 600cm / (31.875cm/s + 58.012cm/s ) = 6.674s
      5. T*Vcmv1 = Distance-from-0
      6. (equation #5 with numbers plugged in) 6.674s * 31.875cm/s = 212.734cm
   2. At 600 cm after 6.674 s they will collide at 212.734 cm
   3. Graph Equations
      1. First CMV = Vcmv1*X = Y
      2. Second CMV = -Vcmv2*X + Distance-apart = Y
   4. Graph
      1. 
2. Find the position where the faster CMV will catch up with the slower CMV if they start at least 1 m (100cm) apart, move in the same direction, and start simultaneously.
   1. Equation:
      1. Vcmv-slow*T + Distance-apart = Vcmv-fast*T
      2. T*(Vcmv-slow - Vcmv-fast) = -Distance-apart
      3. -Distance-apart / (Vcmv-slow - Vcmv-fast) = T
      4. (or if you like more positive numbers) Distance-apart / (Vcmv-fast - Vcmv-slow) = T
      5. (equation #4 with numbers plugged in) 100cm / (58.021cm/s - 31.875cm/s) = 3.824s
      6. T*Vcmv-fast = Distance-traveled
      7. (equation #6 with numbers plugged in) 3.824s * 58.021 cm/s = 221.911cm
   2. At 1m (100cm) after 3.824s they will collide at 221.911cm
   3. Graph Equations
      1. Vcmv-fast*T = Y
      2. Vcmv-slow*X + Distance-apart = Y
   4. Graph
      1. 

Procedure

• To test where two CMVs placed 600cm apart and traveling toward each other would collide we measured 600cm of floor using a measuring tape and proceeded to have two CMVs, 600cm apart, drive toward each other until the collided. We then recorded the point where they collided, we repeated this test five times for accuracy.
• To test where two CMVs placed 100cm apart and traveling in the same direction at different rates other would collide we measured 100cm of floor using a measuring tape and proceeded to have two CMVs, 100cm apart, drive in the same direction until they collided. We then recorded the point where they collided, we repeated this test five times for accuracy.
  
  

Data Gathered

Distance from origin where CMVs colided


Predictions: 212.734cm 221.911cm

Analysis
Both our experimental results were above our predicted results by 10.98% and 3.91% respectively. These numbers drop to 6.89% and 0.54% when the outliers (in bold) are factored out. This increase could easily have been due to a lessening in the voltage of the batteries of the faster CMV, both the collision and catch up would have gone over more distance if it moved at a slower pace.

Discussion questions

1. Where would the cars meet if their speeds were exactly equal?
   1. If heading toward each other they would meet at exactly 1/2 the distance they were apart, if going in the same direction they would never meet.
2. Sketch position-time graphs to represent the catching up and crashing situations. Show the point where they are at the same place at the same time.
   1. See graphs above in first section.
3. Sketch velocity-time graphs to represent the catching up situation. Is there any way to find the points when they are at the same place at the same time?
   1. 
   2. There would be no way to determine when they are at the same point because you can't determine position of an object only knowing it's velocity. If position a nearly any given time was know then the point of intersection could be calculated algebraically.

Conclusion
With a reasonable margin of error our hypothesis of where the cars would meet was correct. They meet at nearly the same distance that we predicted they would, with only a few centimeter margin of error, less then 7% and 1% respectively when outliers are factored out; 212.734cm and 221.911cm respetivly were predicted and 326.094cm and 230.596cm respectivly were the experimental results. A few possible sources of error were that the CMVs didn't go the same speed as when we measured them earlier, the CMVs didn't go straight and as such travled an inaccurate amount of distance, and the CMVS might not have been started at the same time. Some ways we could reduce error in this experiment would be to remeasure the speed of the CMVs before doing our calculations, having the CMVs pull a string that pulled a coasting car so that regardless of the direction that the CMVs traveled they would pull the coasting car straight, or using computers to synchronize when the CMVs started moving.

Week 4 - 9/26 to 9/28

This was a rather eventful week. It was a three day week and I was out for one of the days (Wed the 28th) so there's not much here.

Week 5 - 10/3 to 10/7

10/3/2011 Class Notes Free fall (day I was out)

I was also out the first Monday of this weekm which was today so I missed the class notes on free fall. However from the reading there was very little that was new. From reviewing others notes I determined that there was nothing covered that wasn't covered in the reading, so I chose not to copy notes and plagiarize or copy and paraphrase 2nd hand notes and risk misinterpretation.

10/3/2011 Homework Physics Classroom Lesson 5 Summary Method 1

Introduction
Topic Sentence: Free falling objects, are pulled down by gravity at -9.8m/s/s, they don't encounter air resistance
A free falling object is an object that is falling under the sole influence of gravity.

• Free-falling objects do not encounter air resistance.
• All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s

Acceleration of Gravity
Topic Sentence: g is always -9.8m/s/s, except when it's not.
g = -9.8 m/s/s = the acceleration for any object moving under the sole influence of gravity.

The value of the acceleration of gravity (g) is different in different gravitational environments, eg: other planets
Even on the surface of the Earth, there are local variations in the value of the acceleration of gravity (g). These variations are due to latitude, altitude and the local geological structure of the region.


Representing Free Fall by Graphs
Topic Sentence: When we say g is -9.8m/s/s and it's a measure of acceleration that means exactly what you think it means, also the stuff you learned about acceleration and graphs in chapters 1 and 3 hasn't changed.
In this part of Lesson 5, the motion of a free-falling motion will be represented using x-t and v-t graphs

This is a x-t graph of a free falling object.

A velocity versus time graph for a free-falling object is shown below.

How Fast? and How Far?
Topic Sentence: g = -9.8m/s/s and it works just like any other measure of acceleration in any given equation.


The Big Misconception
Topic Sentence:all objects fall at the same rate, the misconception is due to larger objects having more force to overcome air resistance better.
the acceleration of gravity is the same for all free-falling objects regardless of any given circumstance. Yet the questions are often asked "doesn't a more massive object accelerate at a greater rate than a less massive object?" nearly everyone has observed the difference in the rate of fall of a single piece of paper (or similar object) and a textbook. The two objects clearly travel to the ground at different rates - with the more massive book falling faster.
The answer is no! Assuming you're talking about free-fall. More massive objects will only fall faster if there is an appreciable amount of air resistance present.

The actual explanation of why all objects accelerate at the same rate involves the concepts of force and mass. The acceleration of an object is directly proportional to force and inversely proportional to mass. Increasing force tends to increase acceleration while increasing mass tends to decrease acceleration. Thus, the greater force on more massive objects is offset by the inverse influence of greater mass. Subsequently, all objects free fall at the same rate of acceleration, regardless of their mass.

10/4/2011 Lab What is Acceleration due to Gravity?

Partner: Ryan Luo

Objective
Question: What is Acceleration due to Gravity? What would a v-t graph of a falling object look like?
Hypothesizes: A velocity time graph of a free falling object would look very similar to the graph Y=-9.8x starting at the origin and continuing indefinably.

Procedure
Materials: Spark timer, spark tape, a mass, masking tape

1. Attach a mass to one end of a lengthy piece of spark tape.
2. Running the spark tape trough a spark timer, drop the mass out a window.
3. Measure the position of the dots on the spark tape using measuring tape taped side by side on the ground with spark tape, record and make calculations.
4. Make a v-t graph based on calculations

Data
Spark Tape Measurements


Velocity Calculations


Analysis

• discussion and interpretation of the equations of the graphs
  • The equation of the x-t graph was very similar to ∆d = ViT + .tAT^2 when Vi = 0 and A = g. If g was slightly lower, for example due to friction, then the equation would nearly exactly resemble our graph.
  • The equation of the v-t graph was very similar to Vf = ViT + AT when Vi is very low and A is g. If g was slightly lower, for example due to friction, then the equation would nearly exactly resemble our graph.
• % error and % difference
  • % error = 10.49%
  • % difference = 9.97%
• Sample calculations of velocity, % error, and % difference
  • Velocity
    • (X-final - X-initial) / (T-final - T-initial) = velocity at the mid time between T-final and T-initial
    • The above is assuming constant acceleration
    • Eg: (17.41 - 0.00) / (0.1 - 0.0) = 174.1 cm/s
  • % error
    • (Expected-result - Actual-result) / Actual-result = % error
    • Eg: ((981 cm/s/s - 887.79 cm/s/s) / 887.79 cm/s/s) * 100 = 10.49%
  • % difference
    • (Expected-result - Actual-result) / ((Expected-result + Actual-result) / 2)
    • Eg: ((981 cm/s/s - 887.76 cm/s/s ) / ((981 cm/s/s + 887.76 cm/s/s) / 2)) * 100 = 9.97%

Discussion

1. Does the shape of your v-t graph agree with the expected graph? Why or why not?
   1. The general shape of our v-t graph is very similar to what we would expect however the slope is not as steep as we expected. This means that the acceleration was not as high as we expected, this was most likely due to friction in many places on the spark tape.

1. Does the shape of your x-t graph agree with the expected graph? Why or why not?
   1. Similar to the v-t graph the shape of the graph is correct but the slope is not as steep as we expected. Again this was due to a lower acceleration then we expected and was most likely due to the same friction that was present in the spark tape above.

1. How do your results compare to that of the class? (Use Percent difference to discuss quantitatively.)
   1. Our results were closer to the expected result then the majority of the rest of the class with a percent difference of 9.97% compared to the class's 15.55% percent difference.

1. Did the object accelerate uniformly? How do you know?
   1. Yes, aside from a small blip in our data the increase in velocity, slope of the v-t graph, or acceleration (however you want to see it) is constant, indicating uniform acceleration.

1. What factor(s) would cause acceleration due to gravity to be higher than it should be? Lower than it should be?
   1. Factors like friction on the spark tape or air resistance would cause acceleration due to gravity to be lower then it should be, factors like increased tectonic activity could cause acceleration due to gravity to be higher or lower then it should be as well.

Conclusion
We were not able to accurately calculate acceleration due to gravity; due to several possible errors in our procedure, our calculations were below the target number. We believe the largest source of error was the friction between the spark tape, spark timer, and whatever else it was touching. In addition, air resistance and kinks in the spark tape could have also contributed to error. We could have minimized the amount of error due to friction by increasing the mass of the weight we dropped attached, so there would me more force pulling the spark tape to better overcome friction, we could have also lubricated the contact points to minimize friction. To minimize error from air resistance we could have performed the test in a vacuum. To minimize error from kinks in the tape we could have, using more space, laid out a long strip of straight spark tape to cleanly feed in to the spark timer.

Week 6 - 10/10 to 10/12

10/11/2011 Class Notes Reviewing for test

Determine if these statements are true or false

1. The location of an object can be described by stating it's distance from a given point (ignoring direction). False
2. The distance an object ravels and it's displacement are not always the same. True
3. An object's speed an velocity are always the same. False
4. Acceleration always means that an objects is speeding up. False
5. acceleration always occurs in the same direction as an object is moving. False
6. If an object has a speed of zero (even instantaneously), it has no acceleration. False

If and object is accelerating and you know the initial time (but no initial velocity), the final velocity and time, and the distance the object covered between the two points you could use the equation ∆d = 1/2*(Vi-Vt)*T to calculate Vi